The main criterion in investment decisions is to maximize the investors utility. Traditional capital asset pricing models cannot be used when asset returns do not follow a normal distribution. For this reason, we use capital asset pricing model with independent and identically asymmetric power distributed (CAPM-IIAPD) and capital asset pricing model with asymmetric independent and identically asymmetric exponential power distributed with two tail parameters(CAPM-AIEPD) to estimate return and risk. When the assumption of normality is violated, the first and second moments lose their efficiency in optimization and we need to use the third and fourth moments. For the first time, we propose independent and identically asymmetric exponential power distributed with two tail parameters. Then, we use higher moments optimization with unequal weights to optimize portfolios. The results indicate that capital asset pricing model with independent and identically asymmetric power distributed (CAPM-IIAPD) is better than asymmetric independent and identically asymmetric exponential power distributed with two tail parameters(CAPM-AIEPD) to estimate return and risk. Adjusted Sharp ratio in portfolio optimization in second moments are higher than others. Adjusted returns to risk in third and fourth moments in the CAPM-IIAPD model significantly differ from the CAPM-AIEPD model and have a better performance.
